The company has hired a search firm to find a new financial chief and says there will be no IPO until 2019 at the earliest

Airbnb Inc. said its chief financial officer is stepping down, an unexpected move that raises questions about its progress toward a highly anticipated initial public offering, which the home-sharing company said won’t come until 2019 at the earliest.

Laurence Tosi, CFO since July 2015 after holding that role at Blackstone Group, will leave later this month to work on his investment fund, Airbnb said Thursday. Airbnb also said it chief business affairs and legal officer Belinda Johnson will become operating chief, a newly...